Glass horse-shoe kiln temperature prediction method based on gra-woa-gru

Abstract

The application discloses a glass horse shoe kiln temperature prediction method based on GRA-WOA-GRU, comprising the following steps: collecting temperature data set of the horse shoe kiln; preprocessing the working pool temperature data; performing grey correlation analysis on the influence parameter data of the working pool temperature; dividing the data set of the preprocessed working pool temperature data and the influence parameter data with the correlation greater than a preset value to obtain a training set and a test set; establishing a gated recurrent unit model, and optimizing the hyperparameters of the GRU model by using a whale optimization algorithm (WOA) to obtain a WOA-GRU model; and inputting the training set into the WOA-GRU model to perform temperature prediction and obtain a temperature prediction value. The application solves the problem that the existing ML model using a hybrid meta-heuristic algorithm and a data preprocessing technology is used to predict the temperature of the horse shoe kiln, but the ML model is a shallow structure and cannot completely simulate the nonlinear relationship between variables and various complex parameters, resulting in low accuracy of the output prediction result.

Description

Technical Field

[0001] This invention relates to the field of glass horseshoe kiln temperature prediction technology, and in particular to a glass horseshoe kiln temperature prediction method based on GRA-WOA-GRU. Background Technology

[0002] Glass production involves various aspects of life, including food and industry, and is closely related to our daily lives. Furthermore, glass production is a high-energy-consuming industry, generating enormous energy consumption. The glass kiln, as the core equipment in glass production, is crucial to the company's production efficiency and future development benefits, and it also suffers from outdated technology and non-standard operating procedures. Accurate prediction of the horseshoe kiln temperature can serve as guidance for later processes, reduce energy consumption and production costs, and has significant practical implications.

[0003] The firing of glass products in a horseshoe kiln is a nonlinear, multi-coupled, and easily disturbed process. The combustion temperature is high and the environment is complex, making it impossible to directly measure the temperature of the glass products. Therefore, it is necessary to construct a data-driven model to estimate the temperature when there is limited parameter information.

[0004] In recent years, statistical learning and machine learning methods have become widely popular, such as Extreme Learning Machine (ELM), Random Forest (RF), Support Vector Machine (SVM), and Backpropagation Neural Network (BP). These machine learning (ML) models have excellent capabilities for modeling variables and complex nonlinear parameters, thus making them applicable to the field of temperature prediction. Since the hyperparameters of the ML model determine the estimation results and accuracy, metaheuristic algorithms, including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Whale Optimization (WOA), Pollination Algorithm (FPA), and Grey Wolf Optimization (GWO), are employed to obtain the optimal hyperparameters of the ML model. Furthermore, data preprocessing techniques such as Kendall-τ correlation coefficient and entropy weights, KPCA dimensionality reduction, and correlation analysis can be used to find effective input combinations for the ML model.

[0005] ML models using hybrid meta-heuristic algorithms and data preprocessing techniques have higher estimation accuracy than ML models or physics-based methods. Therefore, ML models using hybrid meta-heuristic algorithms and data preprocessing techniques are often used to predict the temperature of horseshoe kilns. However, ML models have a shallow structure and limited learning ability, and cannot fully simulate the nonlinear relationship between variables and various complex parameters, resulting in low accuracy of the output prediction results. Summary of the Invention

[0006] To address the aforementioned shortcomings, this invention proposes a method for predicting the temperature of a glass horseshoe kiln based on GRA-WOA-GRU. The aim is to solve the problem that existing ML models, which use hybrid meta-heuristic algorithms and data preprocessing techniques to predict the temperature of horseshoe kilns, are shallow in structure and have limited learning capabilities. They cannot fully simulate the nonlinear relationships between variables and various complex parameters, resulting in low accuracy of the output prediction results.

[0007] To achieve this objective, the present invention adopts the following technical solution:

[0008] A method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU includes the following steps:

[0009] Step S1: Collect the temperature dataset of the horseshoe kiln, which includes working pool temperature data and working pool temperature influence parameter data;

[0010] Step S2: Preprocess the working pool temperature data to obtain preprocessed working pool temperature data;

[0011] Step S3: Perform grey relational analysis (GRA) on the influence parameter data of the working pool temperature to obtain influence parameter data with a correlation degree greater than the preset value;

[0012] Step S4: Divide the preprocessed working pool temperature data and the influence parameter data with a correlation greater than a preset value into a dataset to obtain a training set and a test set, and set the training set and the test set into a sliding time window format respectively;

[0013] Step S5: Establish a gated recurrent unit (GRU) model and optimize the hyperparameters of the GRU model using the whale optimization algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model.

[0014] Step S6: Input the training set into the WOA-GRU model to predict the temperature and obtain the predicted temperature value;

[0015] Step S7: Based on the predicted temperature values ​​and the test set, calculate the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). 2 The temperature prediction performance of the WOA-GRU model was evaluated.

[0016] Preferably, step S2 specifically includes the following sub-steps:

[0017] Step S21: Standardize the working pool temperature data using the Z-score normalization method to obtain normally distributed temperature data;

[0018] Step S22: Use the 3sigma method to perform outlier detection on the normally distributed temperature data;

[0019] Step S23: Calculate the mean of the two data before and after the outlier, and replace the outlier with the mean to obtain the preprocessed working pool temperature data.

[0020] Preferably, in step S3, a grey relational analysis is performed on the data of parameters affecting the working pool temperature, specifically including the following sub-steps:

[0021] Step S31: Determine the reference sequence reflecting the characteristics of system behavior and the comparison sequence influencing system behavior. The reference sequence reflecting the characteristics of system behavior is used to measure and compare the correlation between the sequences, and is represented as: Y = y(k)|1,2,…,n, where y(k) represents the data value corresponding to the reference sequence; the comparison sequence influencing system behavior is represented as: X i =x i (k)|k=1,2,…,n,i=1,2,…,m,x i (k) represents the k-th value in the i-th comparison sequence, and m represents the number of parameters;

[0022] Step S32: Perform normalization processing. The grey relational coefficient represents the degree of correlation between the ideal value and the normalized value, as shown in the following formula:

[0023]

[0024] Where, |y(k)-x i (k)| is the distance between the reference sequence and the corresponding k-th data in the i-th comparison sequence; Indicates the maximum distance; ξ represents the minimum distance; ρ is called the resolution coefficient, and the value range of ρ is generally (0, 1). When ρ ≤ 0.5463, the resolution is relatively high, and ρ = 0.5 is usually taken; i (k) represents the gray-level correlation coefficient;

[0025] Step S33: Take the average of the gray-level correlation coefficients at each time point and combine them into a single value, namely the gray-level correlation degree, to serve as an indicator of the degree of correlation between the comparison series and the reference series, as shown in the following formula:

[0026]

[0027] Where, r i Let be the gray-level correlation degree of the i-th feature.

[0028] Preferably, in step S5, the hyperparameters of the GRU model are optimized using the Whale Optimization Algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model, which specifically includes the following sub-steps:

[0029] Step S51: Initialize training data;

[0030] Step S52: Set the maximum number of iterations and the number of whales in the Whale Optimization Algorithm (WOA), and set the optimization interval for the number of hidden layer neurons and the step size interval for the sliding time window in the GRU model;

[0031] Step S53: Use WOA to find the optimal number of neurons in the hidden layer of the GRU model within the optimization interval of the number of neurons, and to find the optimal time step within the step size interval of the sliding time window.

[0032] Step S54: Calculate the mean squared error of the training data and use it as the fitness function of the whale;

[0033] Step S55: Update the position of individuals in the whale pod according to the whale's fitness function;

[0034] Step S56: Optimize the weight threshold parameters of the GRU neural network using WOA;

[0035] Step S57: Assign the WOA-optimized weight threshold parameters to the GRU model to obtain the WOA-GRU model.

[0036] Preferably, in step S5, the specific calculation formula for the gated recurrent unit (GRU) model is as follows:

[0037] r t =σ(W r ·[h t-1 ,x t ])

[0038] z t =σ(W z ·[h t-1 ,x t ])

[0039]

[0040]

[0041] Where, r t To reset the door; z t To update the gate; x t This is the current input; This summarizes the current input and the previous hidden layer states; h tFor the output of the hidden layer after updating the memory; W r To reset the weight matrix of the gate; W z To update the weight matrix of the gate; W h σ is the hidden layer weight matrix; σ is the Sigmoid activation function; tanh is the hyperbolic tangent activation function; "*" represents the convolution operator.

[0042] Preferably, in step S7, the specific formula for calculating the mean absolute error (MAE) is as follows:

[0043]

[0044] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0045] The specific formula for calculating the Mean Absolute Percentage Error (MAPE) is as follows:

[0046]

[0047] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0048] The specific formula for calculating the root mean square error (RMSE) is as follows:

[0049]

[0050] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0051] The coefficient of determination (R) 2 The specific calculation formula is as follows:

[0052]

[0053] Where n' is the number of samples; y i These are actual sample values; The mean of the sample; To predict sample values.

[0054] The technical solutions provided in this application embodiment may include the following beneficial effects:

[0055] This approach first uses GRA to perform correlation analysis on temperature-related parameters, identifying factors that significantly impact temperature. Then, WOA is used to optimize the hyperparameters of the GRU deep learning model, achieving the best predictive performance. Compared to shallow-structure ML models, the WOA-optimized GRU deep learning model exhibits better generalization and fitting capabilities for nonlinear data, thus improving the accuracy of prediction results. Attached Figure Description

[0056] Figure 1 This is a flowchart of a method for predicting the temperature of a glass horseshoe kiln based on GRA-WOA-GRU. Detailed Implementation

[0057] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0058] A method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU includes the following steps:

[0059] Step S1: Collect the temperature dataset of the horseshoe kiln, which includes working pool temperature data and working pool temperature influence parameter data;

[0060] Step S2: Preprocess the working pool temperature data to obtain preprocessed working pool temperature data;

[0061] Step S3: Perform grey relational analysis (GRA) on the influence parameter data of the working pool temperature to obtain influence parameter data with a correlation degree greater than the preset value;

[0062] Step S4: Divide the preprocessed working pool temperature data and the influence parameter data with a correlation greater than a preset value into a dataset to obtain a training set and a test set, and set the training set and the test set into a sliding time window format respectively;

[0063] Step S5: Establish a gated recurrent unit (GRU) model and optimize the hyperparameters of the GRU model using the whale optimization algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model.

[0064] Step S6: Input the training set into the WOA-GRU model to predict the temperature and obtain the predicted temperature value;

[0065] Step S7: Based on the predicted temperature values ​​and the test set, calculate the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). 2 The temperature prediction performance of the WOA-GRU model was evaluated.

[0066] This scheme proposes a method for predicting the temperature of glass horseshoe furnaces based on GRA-WOA-GRU, such as... Figure 1As shown, the first step is to collect the temperature dataset of the horseshoe kiln. This dataset includes working pool temperature data and influencing parameter data. Specifically, the working pool temperature data and influencing parameter data are collected using temperature sensors in the horseshoe kiln. These influencing parameters include natural gas total pressure, pressure reducing valve pressure, gas pressure, gas flow rate, gas calorific value, secondary air pressure and flow rate, radiation temperature, regenerator arch temperature, pool bottom temperature, and total flue temperature. The second step is to preprocess the working pool temperature data to obtain preprocessed data. Specifically, the working pool temperature data undergoes 3-sigma outlier detection, and outliers are replaced with the mean of the preceding and following data. This helps ensure the accuracy and completeness of the temperature data. The third step is to perform grey relational analysis (GRA) on the influencing parameter data of the working pool temperature to obtain parameters with a correlation degree greater than a preset value. In this embodiment, the preset value is 0.5. Grey relational analysis can select parameters with a greater influence on temperature, improving the prediction efficiency of the subsequent WOA-GRU model. The fourth step involves dividing the preprocessed working pool temperature data and the influence parameter data with a correlation greater than a preset value into a training set and a test set. The training set and the test set are then set to a sliding time window format. Specifically, the training set is used as input to the WOA-GRU model, and the test set is used to test the prediction performance of the WOA-optimized GRU model. In this embodiment, a sliding time window is used to process the training set and the test set separately to compensate for errors caused by the lack of time consideration in conventional temperature prediction models. The fifth step is to establish a gated recurrent unit (GRU) model and optimize the hyperparameters of the GRU model using the Whale Optimization Algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model. Specifically, GRU, as a version of Long Short-Term Memory (LSTM) networks, retains the performance of LSTM while simplifying its construction. The GRU neural network is an improvement on recurrent neural networks (RNNs), effectively overcoming the problems of long dependencies and vanishing gradients in RNNs by introducing a "gate" structure. The Whale Optimization Algorithm (WOA) is a metaheuristic algorithm. Its core principle is to mimic the hunting behavior of whale pods, which consists of three stages: surrounding prey, swimming and foraging, and bubble-based feeding. By utilizing WOA to optimize the hyperparameters of the GRU model, such as the number of neurons (m) and the sliding time window step size (length), the optimal hyperparameters are sought. This further enhances the predictive performance of the WOA-GRU model while reducing runtime and improving efficiency.The sixth step is to input the training set into the WOA-GRU model for temperature prediction, obtaining the predicted temperature value. Specifically, the GRU network neurons mainly contain two "gate" structures: an update gate and a reset gate. The update gate selectively forgets the hidden state information from the previous time step, while the reset gate selectively remembers the current state and previous information. The closer the values ​​of the update gate and reset gate are to 0, the more information needs to be forgotten from the previous time step; the closer the values ​​of the update gate and reset gate are to 1, the more information is remembered. Therefore, the GRU model can effectively predict data information. In this embodiment, the WOA-optimized GRU model is used. The seventh step is to calculate the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R) based on the predicted temperature value and the test set. 2 The temperature prediction performance of the WOA-GRU model was evaluated using the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²). 2 All of these are model evaluation metrics. Model evaluation metrics are functions based on predicted and actual values. This scheme uses model evaluation metrics to evaluate the performance of the WOA-GRU model. It can be found that the WOA-GRU model has good generalization and fitting ability for nonlinear data. The prediction results output by this model can fit the temperature change trend of the horseshoe kiln working pool well.

[0067] This approach first uses GRA to perform correlation analysis on temperature-related parameters, identifying factors that significantly impact temperature. Then, WOA is used to optimize the hyperparameters of the GRU deep learning model, achieving the best predictive performance. Compared to shallow-structure ML models, the WOA-optimized GRU deep learning model exhibits better generalization and fitting capabilities for nonlinear data, thus improving the accuracy of prediction results.

[0068] Preferably, step S2 specifically includes the following sub-steps:

[0069] Step S21: Standardize the working pool temperature data using the Z-score normalization method to obtain normally distributed temperature data;

[0070] Step S22: Use the 3sigma method to perform outlier detection on the normally distributed temperature data;

[0071] Step S23: Calculate the mean of the two data before and after the outlier, and replace the outlier with the mean to obtain the preprocessed working pool temperature data.

[0072] In this embodiment, before preprocessing, the working pool temperature data needs to conform to a normal distribution. However, most working pool temperature data does not meet this requirement. Therefore, the Z-score standardization method is used to standardize the working pool temperature data to obtain normally distributed temperature data. Z-score standardization is a type of data processing called Z-standardization, also known as standard deviation standardization. This method standardizes the data by taking the mean and standard deviation of the original data. The processed data conforms to a standard normal distribution, i.e., the mean is 0 and the standard deviation is 1. After using the 3sigma method to test the normally distributed temperature data, outliers are processed. The 3sigma method is the Raida criterion, which assumes that a set of test data contains only random errors, calculates the standard deviation, determines an interval with a certain probability, and considers any error exceeding this interval as gross error rather than random error. Data containing such errors should be removed. Therefore, the 3sigma method is used to remove outliers.

[0073] Preferably, in step S3, a grey relational analysis is performed on the data of parameters affecting the working pool temperature, specifically including the following sub-steps:

[0074] Step S31: Determine the reference sequence reflecting the characteristics of system behavior and the comparison sequence influencing system behavior. The reference sequence reflecting the characteristics of system behavior is used to measure and compare the correlation between the sequences, and is represented as: Y = y(k)|1,2,…,n, where y(k) represents the data value corresponding to the reference sequence; the comparison sequence influencing system behavior is represented as: X i =x i (k)|k=1,2,…,n,i=1,2,…,m,x i (k) represents the k-th value in the i-th comparison sequence, and m represents the number of parameters;

[0075] Step S32: Perform normalization processing. The grey relational coefficient represents the degree of correlation between the ideal value and the normalized value, as shown in the following formula:

[0076]

[0077] Where, |y(k)-x i (k)| is the distance between the reference sequence and the corresponding k-th data in the i-th comparison sequence; Indicates the maximum distance; ξ represents the minimum distance; ρ is called the resolution coefficient, and the value range of ρ is generally (0, 1). When ρ ≤ 0.5463, the resolution is relatively high, and ρ = 0.5 is usually taken; i (k) represents the gray-level correlation coefficient;

[0078] Step S33: Take the average of the gray-level correlation coefficients at each time point and combine them into a single value, namely the gray-level correlation degree, to serve as an indicator of the degree of correlation between the comparison series and the reference series, as shown in the following formula:

[0079]

[0080] Where, r i Let be the gray-level correlation degree of the i-th feature.

[0081] In this embodiment, since the temperature of the ceramic roller kiln is affected by many factors, the grey relational analysis method is used to analyze multiple influencing factors. The strength of the correlation between parameters is determined based on the degree of difference or similarity in the changing trends of each parameter. Because the parameters have inconsistent dimensions, the mean method is used to perform dimensionless processing of the data before performing the grey relational analysis, as shown in the following formula:

[0082]

[0083] In the formula: x i (k) represents the dimensionless sample of the kth feature in the i-th feature; is the mean of the i-th feature; (k) is the k-th sample in the i-th feature.

[0084] In grey relational analysis, it is necessary to determine a reference series reflecting the behavioral characteristics of the system and a comparison series influencing the system's behavior. The grey relational coefficients obtained through calculation are too scattered, as they represent the degree of correlation between each value in the comparison series and its corresponding value in the reference series, making comprehensive comparisons difficult. Therefore, it is necessary to average the correlation coefficients at each time point and consolidate them into a single value, the relational degree, to serve as an indicator of the degree of correlation between the comparison series and the reference series.

[0085] Preferably, in step S5, the hyperparameters of the GRU model are optimized using the Whale Optimization Algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model, which specifically includes the following sub-steps:

[0086] Step S51: Initialize training data;

[0087] Step S52: Set the maximum number of iterations and the number of whales in the Whale Optimization Algorithm (WOA), and set the optimization interval for the number of hidden layer neurons and the step size interval for the sliding time window in the GRU model;

[0088] Step S53: Use WOA to find the optimal number of neurons in the hidden layer of the GRU model within the optimization interval of the number of neurons, and to find the optimal time step within the step size interval of the sliding time window.

[0089] Step S54: Calculate the mean squared error of the training data and use it as the fitness function of the whale;

[0090] Step S55: Update the position of individuals in the whale pod according to the whale's fitness function;

[0091] Step S56: Optimize the weight threshold parameters of the GRU neural network using WOA;

[0092] Step S57: Assign the WOA-optimized weight threshold parameters to the GRU model to obtain the WOA-GRU model.

[0093] In this embodiment, the weight threshold parameters of the GRU neural network are optimized by WOA, thereby establishing a stable WOA-GRU model and improving prediction accuracy and generalization ability.

[0094] To further explain, after obtaining the WOA-GRU model, it needs to be trained using the gradient descent algorithm. Gradient descent is currently the most popular optimization strategy, used in machine learning and deep learning. It is used during model training, can be combined with various algorithms, and is easy to understand and implement. Gradient descent is a classic algorithm for finding local minima. Its main purpose is to iteratively update the model parameters along the negative gradient, gradually converging the objective function to a local minimum.

[0095] Preferably, in step S5, the specific calculation formula for the gated recurrent unit (GRU) model is as follows:

[0096] r t =σ(W r ·[h t-1 ,x t ])

[0097] z t =σ(W z ·[h t-1 ,x t ])

[0098]

[0099]

[0100] Where, r t To reset the door; z t To update the gate; x t This is the current input; This summarizes the current input and the previous hidden layer states; h t For the output of the hidden layer after updating the memory; W r To reset the weight matrix of the gate; Wz To update the weight matrix of the gate; W h σ is the hidden layer weight matrix; σ is the Sigmoid activation function; tanh is the hyperbolic tangent activation function; "*" represents the convolution operator.

[0101] In this embodiment, the GRU model, compared with the traditional shallow structure ML model, has good generalization and fitting ability for nonlinear data, which can improve the accuracy of prediction results.

[0102] To further explain, the input to the GRU model is the input x at time t. t and the hidden state x at time t-1 t-1 This contains information from the prior nodes. The output is the output y of the hidden node at time t. t and the hidden state h that is transferred to the next node t .

[0103] The GRU model is an improvement on the Recurrent Neural Network (RNN) model, effectively overcoming the problems of long dependencies and vanishing gradients in RNNs by introducing a "gate" structure. The GRU model retains only two gates: the update gate and the reset gate. Specifically, the update gate controls the amount of past state information to be included in the current state. A higher update gate value allows more information from previous states to be passed to the current state. On the other hand, the reset gate determines the amount of previous state information to ignore. A lower reset gate value indicates less state information is discarded.

[0104] Preferably, in step S7, the specific formula for calculating the mean absolute error (MAE) is as follows:

[0105]

[0106] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0107] The specific formula for calculating the Mean Absolute Percentage Error (MAPE) is as follows:

[0108]

[0109] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0110] The specific formula for calculating the root mean square error (RMSE) is as follows:

[0111]

[0112] Where n' is the number of samples; y i These are actual sample values; To predict sample values;

[0113] The coefficient of determination (R) 2 The specific calculation formula is as follows:

[0114]

[0115] Where n' is the number of samples; y i These are actual sample values; The mean of the sample; To predict sample values.

[0116] In this embodiment, the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (R²) are calculated based on the temperature prediction and the test set. 2 These evaluation metrics, used to assess the performance of the WOA-GRU model, reveal that the WOA-GRU model exhibits good generalization and fitting capabilities for nonlinear data. The prediction results output by this model can effectively fit the changing trend of the working pool temperature in the horseshoe kiln.

[0117] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0118] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU, characterized in that: Includes the following steps: Step S1: Collect the temperature dataset of the horseshoe kiln, which includes working pool temperature data and working pool temperature influence parameter data; Step S2: Preprocess the working pool temperature data to obtain preprocessed working pool temperature data; Step S3: Perform grey relational analysis (GRA) on the influence parameter data of the working pool temperature to obtain influence parameter data with a correlation degree greater than the preset value; Step S4: Divide the preprocessed working pool temperature data and the influence parameter data with a correlation greater than a preset value into a dataset to obtain a training set and a test set, and set the training set and the test set into a sliding time window format respectively; Step S5: Establish a gated recurrent unit (GRU) model and optimize the hyperparameters of the GRU model using the Whale Optimization Algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model. Step S6: Input the training set into the WOA-GRU model to predict the temperature and obtain the predicted temperature value; Step S7: Based on the predicted temperature values ​​and the test set, calculate the mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and coefficient of determination (CQD). ( ), to evaluate the temperature prediction performance of the WOA-GRU model; In step S5, the hyperparameters of the GRU model are optimized using the Whale Optimization Algorithm (WOA) to obtain the WOA-optimized GRU model, i.e., the WOA-GRU model. This specifically includes the following sub-steps: Step S51: Initialize training data; Step S52: Set the maximum number of iterations and the number of whales in the Whale Optimization Algorithm (WOA), as well as the optimization interval for the number of hidden layer neurons in the GRU model and the step size interval for the sliding time window; Step S53: Use WOA to find the optimal number of neurons in the hidden layer of the GRU model within the optimization interval of the number of neurons, and to find the optimal time step within the step size interval of the sliding time window. Step S54: Calculate the mean squared error of the training data and use it as the fitness function of the whale; Step S55: Update the position of individuals in the whale pod according to the whale's fitness function; Step S56: Optimize the weight threshold parameters of the GRU neural network using WOA; Step S57: Assign the WOA-optimized weight threshold parameters to the GRU model to obtain the WOA-GRU model.

2. The method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU according to claim 1, characterized in that: Step S2 specifically includes the following sub-steps: Step S21: Standardize the working pool temperature data using the Z-score normalization method to obtain normally distributed temperature data; Step S22: Use the 3sigma method to perform outlier detection on the normally distributed temperature data; Step S23: Calculate the mean of the two data before and after the outlier, and replace the outlier with the mean to obtain the preprocessed working pool temperature data.

3. The method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU according to claim 1, characterized in that: In step S3, a grey relational analysis is performed on the data of parameters affecting the working pool temperature, specifically including the following sub-steps: Step S31: Determine the reference sequence reflecting the characteristics of system behavior and the comparison sequence influencing system behavior. The reference sequence reflecting the characteristics of system behavior is used to measure and compare the correlation between the sequences, and is expressed as: The reference sequence represents the data values; the comparison sequence that affects the system behavior is represented as: Let represent the k-th value in the i-th comparison sequence, and m represent the number of parameters; Step S32: Perform normalization processing. The grey relational coefficient represents the degree of correlation between the ideal value and the normalized value, as shown in the following formula: in, It is the distance between the reference sequence and the k-th data point in the i-th comparison sequence; Indicates the maximum distance; This represents the minimum distance; ρ is called the resolution coefficient, and the value range of ρ is generally (0, 1). When ρ≤0.5463, the resolution is relatively high, and ρ is usually taken as 0.

5. Represents the gray-scale correlation coefficient; Step S33: Take the average of the gray-level correlation coefficients at each time point and combine them into a single value, namely the gray-level correlation degree, to serve as an indicator of the degree of correlation between the comparison series and the reference series, as shown in the following formula: in, Let be the gray-level correlation degree of the i-th feature.

4. The method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU according to claim 1, characterized in that: In step S5, the specific calculation formula for the gated recurrent unit (GRU) model is as follows: in, To reset the door; To update the door; This is the current input; Summarize the current input and the previous hidden layer states; The output of the hidden layer after updating the memory; To reset the weight matrix of the gate; To update the weight matrix of the gate; Here is the hidden layer weight matrix; σ is the sigmoid activation function; tanh is the hyperbolic tangent activation function. "" indicates the convolution operator.

5. The method for predicting the temperature of a glass horseshoe furnace based on GRA-WOA-GRU according to claim 1, characterized in that: In step S7, the specific formula for calculating the mean absolute error (MAE) is as follows: Where n' is the number of samples; These are actual sample values; To predict sample values; The specific formula for calculating the Mean Absolute Percentage Error (MAPE) is as follows: Where n' is the number of samples; These are actual sample values; To predict sample values; The specific formula for calculating the root mean square error (RMSE) is as follows: Where n' is the number of samples; These are actual sample values; To predict sample values; The coefficient of determination ( The specific calculation formula is as follows: Where n' is the number of samples; These are actual sample values; The mean of the sample; To predict sample values.

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